Processing signals comprises in a variety of systems a channel equalization. A channel equalization is employed for compensating the effects of a fading multipath channel, which constitute a fundamental problem in communication systems.
Various channel equalization techniques have been developed for the traditional single-carrier transmission systems and more recent CDMA systems. With increasing data rates and signal bandwidths in new and future systems, there is moreover an increasing interest in multicarrier transmission techniques, for which dedicated channel equalization techniques have to be employed. In a multicarrier transmission system, a transmitted higher-rate data stream is divided into a number of lower-rate sub-channels partly overlapping in the frequency domain. For multiplexing and demultiplexing these sub-channels, various techniques are known, for instance orthogonal Frequency Division Multiplexing (OFDM) techniques and Filter Bank based Multicarrier (FBMC) techniques. FBMC techniques are sometimes also referred to as Discrete Wavelet Multitone (DWMT) techniques.
OFDM has been described for example by R. van Nee and R. Prasad in chapter 2 “OFDM basics” of the document “OFDM Wireless Multimedia Communications”, Artech House, London, 2000. In an OFDM system and its baseband version Discrete Multitone (DMT), a high-rate data stream is split into a number of lower rate streams that are transmitted simultaneously over a number of sub-carriers, in order to decrease the relative amount of dispersion in time caused by multipath delay spread. The sub-channels are multiplexed and demultiplexed by means of an IFFT-FFT (Inverse Fast Fourier Transform/Fast Fourier Transform) pair. In OFDM and DMT systems, a time-domain guard interval introduced for every OFDM symbol and a simple 1-tap frequency domain equalization is commonly used for channel equalization. In the guard time, the OFDM symbol is cyclically extended to avoid inter-carrier-interference.
OFDM and DMT systems are very robust from a channel equalization point of view. On the other hand, there are certain advantages that can be obtained by using an FBMC system instead of an IFFT-FFT pair, as will be explained in the following.
An FBMC system has been presented for example by T. Ihalainen, Tobias Hidalgo-Stitz and Markku Renfors in: “On the performance of low-complexity ASCET-equalizer for a complex transmultiplexer in wireless mobile channel” in Proc. 7th Int. OFDM-Workshop 2002, Harburg, Germany, pp. 122-126, September 2002.
FIG. 1 is a block diagram of a 0th order ASCET (Adaptive sine-modulated/cosine-modulated filter bank equalizers for transmultiplexers) equalizer structure for complex systems, which was taken from the above cited document “On the performance of low-complexity ASCET-equalizer for a complex transmultiplexer in wireless mobile channel”. The system comprises a transmitting end and a receiving end, between which a multicarrier radio communication is to be enabled.
In order to achieve a good spectral efficiency in radio communications, it is necessary to have a complex I/Q baseband model for the FBMC system. The equalizer structure of FIG. 1 therefore comprises at the transmitting end a synthesis bank for converting 2M real low-rate sub-channel signals for transmission into a complex I/Q (In phase/Quadrature) presentation of a high-rate channel signal. The sampling rate conversion factor is M. The synthesis filter bank includes a cosine modulated filter bank (CMFB) 10, in which sub-filters are formed by modulating a real low-pass prototype filter with a cosine sequence. The cosine-modulation translates the frequency response of the prototype filter around a new center frequency. The synthesis filter bank moreover comprises a sine modulated filter bank (SMFB) 11, in which corresponding sub-filters are formed by modulating a real low-pass prototype filter with a sine sequence.
The equalizer structure further comprises at the receiving end an analysis bank for converting a received high-rate channel signal into low rate sub-channel signals again. A complex critically sampled perfect reconstruction (PR) analysis bank would equally include a corresponding CMFB and a corresponding SMFB, which take the real part of the signal after the complex sub-channel filtering. The prototype filter can be optimized in such a manner that the filter bank satisfies the PR condition, i.e. the analysis transform is invertible by the synthesis transform. In the structure of FIG. 1, however, the analysis bank implements a filter bank with complex output signals instead of real output signals by employing two CMFBs 12, 14 and two SMFBs 13, 15. This way, oversampled sub-channel signals can be obtained for enabling a channel equalization.
The exact equations realized by the CMFBs 10, 12, 14 and the SMFBs 11, 13, 15 can be taken from the above cited document “On the performance of low-complexity ASCET-equalizer for a complex transmultiplexer in wireless mobile channel”.
For a transmission, 2M low-rate symbol sequences, which are to be transmitted on respective sub-channels, are fed to the synthesis filter bank of the transmitting end, half of them corresponding to sub-channels between 0 and fs/2, and the other half corresponding to sub-channels between 0 and −fs/2, where fs is the high sampling rate. More specifically, the sum of a respective pair of symbols Ik(m) and I2M-1-k(m), where k=0, 1, . . . , M−1, is divided by two and fed to the CMFB 10, while the difference between the respective pair of symbols Ik(m) and I2M-1-k(m) is divided by two and fed to the SMFB 11. In the notation Ik(m) and I2M-1-k(m), the indices k and 2M-1-k indicate the respective sub-channel, while the parameter m is a time index. The output of the SMFB 11 is multiplied by j and then combined with the output of the CMFB 10 in order to form a complex I/Q channel signal for transmission. The multiplication by j means that the signal output by the SMFB 11 is used as the quadrature component in the subsequent processing. The units required for the described processing at the transmitting end, including summing means, multiplication means, the CMBF 10 and the SMBF 11, will also be referred to as synthesis portion 20, which is indicated in FIG. 1 by a first rectangle with dashed lines.
The radio channel used for transmission is equivalent to a low-pass channel H1p(z).
At the receiving end, the high-rate channel signal is separated again into a real part Re{.} and an imaginary part Im{.}, the real part Re{.} being fed to the first CMFB 12 and the first SMFB 13 of the analysis bank, and the imaginary part Im{.} being fed to the second CMFB 14 and the second SMFB 15 of the analysis bank. Each of the CMFBs 12, 14 and the SMFBs 13, 15 outputs M signals via M sub-filters.
Each output signal of the second SMFB 15 is added to the corresponding output signal of the first CMFB 12, resulting in a first group of signals, which constitute an in-phase component I of the first M sub-channel signals. Each output of the first SMFB 13 is subtracted from the corresponding output of the second CMFB 14, resulting in a second group of signals, which constitute a quadrature component Q of the first M sub-channel signals. Each output of the first SMFB 13 is added to the corresponding output of the second CMFB 14, resulting in a third group of signals, which constitute a quadrature component Q of the second M sub-channel signals. Each output of the second SMFB 15 is subtracted from the corresponding output of the first CMFB 12, resulting in a fourth group of signals, which constitute an in-phase component I of the second M sub-channel signals. The units required for the processing at the receiving end described so far, including separation means, the CMBFs 12, 14, the SMBFs 13, 15 and summing means, will also be referred to as analysis portion 21, which is indicated in FIG. 1 by a second rectangle with dashed lines.
For channel equalization, a dedicated single real coefficient ck, sk, c2M-1-k, s2M-1-k is then used for weighting the in-phase component I and the quadrature component Q of each sub-channel signal in order to adjust the amplitude and phase of each sub-channel by a simple multiplication. The indices k, 2M-1-k indicate the sub-channel to which the respective coefficient is associated. The coefficients ck, sk, c2M-1-k, s2M-1-k provided for a sub-channel are preferably related to the channel response within the corresponding sub-channel bandwidth.
It is mentioned in the above cited document “On the performance of low-complexity ASCET-equalizer for a complex transmultiplexer in wireless mobile channel” that such a constant coefficient works well only in the case when the frequency response is rather flat within each sub-channel bandwidth, which may require a relatively high number of sub-channels. It is further indicated that higher-order ASCETs may be obtained by including low-order Finite Impulse Response (FIR) filter stages for each of the sub-channels. Such an approach, in which FIR filters are used as equalizers which are adjusted using common adaptation algorithms and criteria, like a mean-squared error criterion, has been described for example by B. Hirosaki in “An analysis of automatic equalizers for orthogonally multiplexed QAM systems”, IEEE Trans. Commun., vol. 28, pp. 73-83, January 1980.
The real parts of corresponding weighted signals of the first and the second group of sub-channel signals are then taken at a respective unit 16 provided to this end and subjected to a respective decision device 18, a so called slicer, in order to obtain the first M real sub-channel symbol sequences Îk(m). The real parts of corresponding weighted signals of the third and the fourth group of sub-channel signals are equally taken at a respective unit 17 provided to this end and subjected to a respective slicer 19, in order to obtain the second M real sub-channel symbol sequences Î2M-1-k(m).
The main characteristic of FBMC systems is that the sub-channels can be designed optimally in the frequency domain, e.g. to have good spectral containment. There are certain advantages that can be obtained by using filter banks with highly frequency selective sub-channels in the transmultiplexer configuration instead of an IFFT-FFT pair, as in the case of OFDM and DMT systems.
Firstly, the bank selectivity is a design parameter for precise spectrum control. This provides resistance against narrowband interference and allows the use of very narrow guard bands around the multicarrier signal. Secondly, the guard period applied in OFDM-systems to combat inter-symbol-interference (ISI) becomes unnecessary. Reducing the frequency-domain guard-band and avoiding the time-domain guard interval saves significant amount of bandwidth for data transmission, thus improving the spectral efficiency. Furthermore, an FBMC system with a proper channel equalization allows the use of a considerably lower number of sub-carriers than the OFDM techniques. This helps to reduce the problems in OFDM which are due to a high peak-to-average power ratio. Being able to use fewer sub-channels to cover the user signal band helps to reduce the latency of the transmission link, improves the performance in case of time-selective channels due to a reduced symbol length, reduces the sensitivity to Doppler effects, frequency errors and phase noise, and gives more freedom in choosing the essential system parameters.
However, the known channel equalization solutions for FBMC systems, in which case the guard-interval approach cannot be used, suffer from insufficient performance, as in the case of the presented 0th order ASCET and/or from relatively high implementation complexity, as in the case of an FIR based approach.
Another structure using a filter bank system which relies on an efficient sub-band processing is the analysis-synthesis (AS) filter bank configuration. In an AS configuration, which can be employed for various coding and adaptive signal processing applications, the signal frequency band is divided in an analysis bank into a number of overlapping sub-bands for processing, and after processing the signal is restored in a synthesis bank by combining the sub-band signals again. In perfect-reconstruction systems, the filter bank design is such that the original signal can be restored completely, if no processing is done in between. In most applications, the system performance can be improved by increasing the number of sub-bands. However, increasing the number of sub-bands increases the implementation complexity, as well as the processing latency due to the filter banks. The use of the AS configuration in channel equalization in single-carrier systems has been dealt with for example by D. Falconer et al. in “Frequency domain equalization for single-carrier broadband wireless systems”, IEEE Communications Magazine, vol. 40, no. 4, April 2002, pp. 58-66.
In order to avoid the above mentioned problems, it has been proposed for a filter-bank based signal processing system in general to process oversampled lower-rate sub-channel signals with a polynomial model of a system frequency response within the frequency range of the respective sub-channel. The polynomial model may comprise in particular an amplitude response model and a phase response model for each sub-channel. A filter structure may then comprise an amplitude equalizer using the amplitude response model for processing a respective sub-channel and an allpass filter using the phase response model for processing a respective sub-channel.
The use of a polynomial frequency response model for a channel equalization allows to approximate the ideal frequency response model with a good performance using a considerably lower number of sub-bands than a 0th order equalizer, in which amplitude and phase are assumed to be constant within each sub-band. In comparison to other FBMC approaches with higher-order equalizers, like in the above mentioned document “An analysis of automatic equalizers for orthogonally multiplexed QAM systems”, using a low-order polynomial frequency response model for an equalizer reduces the complexity and/or improves the performance of the channel estimation by reducing the number of parameters that are to be estimated. In case of a direct adaptive equalization, the approach moreover improves the convergence speed. The approach using a polynomial frequency response model thus provides in general a better tradeoff between performance and complexity than the conventional channel equalization methods for FBMC systems. Simulation results indicate that by using a piece-wise linearly frequency dependent model for the channel frequency response in the channel equalization along with the mentioned equalizer structure, a considerable reduction in the number of sub-channels of up to a factor of about 10 is possible in comparison to the basic OFDM systems.
Nevertheless, some effort is required in this approach for determining the polynomial frequency response model for each sub-channel.